Advanced Database Management System - Tutorials and Notes: Covers for functional dependencies - what is cover set

## Cover set

Given 2 sets of functional dependencies F and G, the set of functional dependencies F is the cover of the set of functional dependencies G if every functional dependency in the set G can be inferred (derived) from the functional dependencies in the set F.

Example 1:
Let R (A, B, C, D, E, F) is a relation with set of functional dependencies F = { A BC, D DF } and G = { A B }.

Does F cover G?
If set of FDs of G can be inferred from F, then we would say that F covers G.
The FD A B of G can be inferred from the FD A BC of F.
No more functional dependencies are there in G. Hence, F covers G.

Does G cover F?
If set of FDs of F can be inferred from G, then we would say that G covers F.
No functional dependencies of F can be inferred from the FD A B of G.
Hence, G does not cover F.

Example 2:
Let R (A, B, C, D, E) be a relation with set of functional dependencies F = { A BC, A D, CD E } and G = { A BCE, A ABD, CD E }.

Does F cover G?
If set of FDs of G can be inferred from F, then we would say that F covers G.
The FD A BCE of G can be inferred from the FDs A BC, A D, and CD E of F. [here, A gives BCD. If you know C and D then E can be derived]
The FD A ABD of G can be inferred from the FDs A BC, and A D of F.
The FD CD E of G can be inferred from the FD CD E of F.
All the three FDs of G can be inferred from FDs of F. Hence, F covers G.

Does G cover F?
If set of FDs of F can be inferred from G, then we would say that G covers F.
The FD A BC of F can be inferred from the FD A BCE of G.
The FD A D of F can be inferred from the FD A ABD of G.
The FD CD E of F can be inferred from the FD CD E of G.
All the three FDs of F can be inferred from FDs of G. Hence, G covers F.

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